Simplify the following expression: $q = \dfrac{8x + 6}{5x + 4} \div \dfrac{1}{3}$
Solution: Dividing by a number is the same as multiplying by its inverse. $q = \dfrac{8x + 6}{5x + 4} \times \dfrac{3}{1}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{(8x + 6) \times 3} {(5x + 4) \times 1}$ $q = \dfrac{24x + 18}{5x + 4}$